Braid variety cluster structures, I: 3D plabic graphs
Combinatorics
2024-05-31 v3 Algebraic Geometry
Rings and Algebras
Representation Theory
Abstract
We introduce -dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type braid varieties. Our results include known cluster structures on open positroid varieties and double Bruhat cells, and establish new cluster structures for type open Richardson varieties.
Keywords
Cite
@article{arxiv.2210.04778,
title = {Braid variety cluster structures, I: 3D plabic graphs},
author = {Pavel Galashin and Thomas Lam and Melissa Sherman-Bennett and David Speyer},
journal= {arXiv preprint arXiv:2210.04778},
year = {2024}
}
Comments
v2: removed some arguments which appear in greater generality in the follow up paper arXiv:2301.07268. v3: Fixed minor typos